{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Data Analytics \n",
    "\n",
    "### Fitting Parametric Distributions  in Python \n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, The University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Analytics: Fitting Parametric Distributions\n",
    "\n",
    "Here's a demonstration of fitting parametric distributions in Python. This demonstration is part of the resources that I include for my courses in Spatial / Subsurface Data Analytics at the Cockrell School of Engineering at the University of Texas at Austin.  \n",
    "\n",
    "#### Parametric Distributions\n",
    "\n",
    "We will cover fitting the following distribution:\n",
    "\n",
    "* Gaussian\n",
    "\n",
    "For more information about working with parametric distributions in Python see this [demonstration](https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/PythonDataBasics_ParametricDistributions.ipynb).\n",
    "\n",
    "\n",
    "I have a lecture on these parametric distributions available on [YouTube](https://www.youtube.com/watch?v=U7fGsqCLPHU&t=1687s).  \n",
    "\n",
    "#### Fitting Parametric Distributions\n",
    "\n",
    "With distribution fitting we are maximizing the likelihood function, $L(\\theta)$:\n",
    "\n",
    "\\begin{equation}\n",
    "L(\\theta) = \\prod^{n}_{\\alpha=1} f\\left(x_{\\alpha} | \\theta \\right)\n",
    "\\end{equation}\n",
    "\n",
    "the product sum of the probablity of the data, $f\\left(x_{\\alpha}\\right)$ over all the data $\\alpha = 1,\\ldots,n$, given the set of distribution parameters, $\\theta$. \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You will need to copy the data file to your working directory.  They are available here:\n",
    "\n",
    "* Tabular data - unconv_MV_v4.csv at https://git.io/fhHLT.\n",
    "\n",
    "#### Importing Packages\n",
    "\n",
    "We will need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # for plotting\n",
    "from scipy import stats                   # summary statistics\n",
    "import math                               # trigonometry etc.\n",
    "import random                             # for randon numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the Working Directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"c:/PGE383\")                     # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Guassian Distribution\n",
    "\n",
    "Let's now use the Gaussian parametric distribution.\n",
    "\n",
    "* we assume the parameters, mean and the variance\n",
    "\n",
    "We will demonstrate the use of the parametric distribution with the forward, $f_x(x)$ and $F_x(x)$, and reverse, $F^{-1}_x(x)$, operations and calculate the summary statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.15.\n",
      "The variance is 0.0009.\n"
     ]
    },
    {
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sW9egzlAABUrhqaekrVtzY/37S0OHppNPv35hLdB8jAIFAKA8fvMbacuW3FiXLtL556eTDwAA1eDii+NnT3z1q9LAgcnng5pFARQohULT382SzyX7+vkogAIAUHrPPRc2P8r3sY9Ju+6afD4AAFSDhx6S7rorGn/f+6STTko+H9Q0CqBAKVTS+p/N4qbfP/qo5J58LgAA1Cp36ZJLovGdd5bOPjvxdAAAqArr18dPfe/VK+wGn+ZgItQkCqBAR61YIS1YEI2nXQDdf3+pc+fc2IoV0quvppMPAAC16L77pDlzovHPfU7q2TP5fAAAqAaXXy4tWxaNn39+WNINKDEKoEBHPflkNLbnnmHkR5q6dZP22Scaf+KJ5HMBAKAWNTVJl10WjQ8bJp18cvL5AABQDebPl268MRo/+GDpAx9IPh/UBQqgQEc99VQ0Nn588nnEOeCAaCwuXwAA0HbTp0uvvRaNf/nLUmNj4ukAAFDxmpqkn/wkfM3Wtat00UVMfUfZUAAFOiquoLjffsnnEScuj6efZh1QAAA6qqlJuvLKaPyAA6SJE5PPBwCAanDHHdLzz0fj557Lru8oKwqgQEesWSO98ko0vu++yecSZ+xYqVOn3NiyZdLSpenkAwBArbjrLun116Pxz36W0SsAAMRZu1b6zW+i8WHDpI9+NPl8UFcogAId8cwz0dGUgwenv/5ns27dpDFjonGmwQMA0H7btsWP/pwwIWxCCAAAoq64QnrnnWj8wgujG/gCJUYBFOiISp7+3ixuNCoFUAAA2u+uu6Q33ojGzz03+VwAAKgGr78u3XRTNH7ccXQeIhEUQIGOePrpaKzSCqBx+VAABQCgfbZtk666Kho/8MDK+zcAAACV4tJLQxuarVu3sHEgkAAKoEB7bdokzZ0bjVfazc8++0TXInv9dWnlynTyAQCgmt13H6M/AQBoi8cflx54IBo/5xxpwIDk80FdogAKtNdzz0lbt+bG+vevvJ3revWShg+PxuNGrwIAgMLcpWuvjcYPPLByNkAEAKCSNDWF0Z/5dtlFOuus5PNB3aIACrRXofU/K3Hn17hRqRRAAQBomyefjJ/98elPJ58LAADV4O67pfnzo/HzzkgqWHkAACAASURBVJO6dk0+H9QtCqBAez35ZDRWqaM/4gqgcfkDAIDCrrkmGhszhs0bAACIs2WL9NvfRuOjR0vHH598PqhrFECB9ti2TXr22Wi80tb/bBZXmH3xRWn9+uRzAQCgGi1YID38cDT+8Y9X5uwPAADSduut0pIl0fh//ZfUQDkKyeI3DmiPF16QNm7Mje24Y/xam5VgwIDo2qRNTdKcOenkAwBAtfnLX6KxgQOlo49OPhcAACrdxo3SVVdF44ccIo0fn3w+qHsUQIH2iFv/c999K7sXK250atzPAaBszGySmb1gZi+b2YUxxweb2f1m9pSZzTGzE9LIE0Ce5culadOi8Y99TGpsTD4foEbRTgI15MYbpZUro/Hzzks+F0AUQIH2idtAqFKnvzdjIyQgVWbWKOm3kiZLGiPpTDMbk/eyb0m6yd33k/QRSb9LNksAsW68Udq6NTfWq5c0ZUo6+QA1iHYSqCHr18evm33ccdKIEcnnA4gCKNB27vFTxyt1A6RmcfnNnRvWMwWQhAMlvezuC9x9s6QbJJ2c9xqX1Cvz/U6SYhZNApCozZvDGmb5TjtN6t49+XyA2kU7CdSK66+X1qzJjTU0SJ/7XDr5AKIACrTdW29Jb7+dG+vUSRo1Kp18ijV4cBitku3dd6VXXkknH6D+7CZpYdbzRZlYtu9KOsvMFkmaJumLyaQGoKDp06XVq3NjnTtLZ5yRTj5A7aKdBGrB2rXx62afeGK4JwVSQgEUaKu43d9HjpS6dEk+l7ZoaJDGjo3G434eAOUQt0205z0/U9Kf3H2QpBMkXWtmkbbazM41s9lmNnv58uVlSBXAv910UzR27LHSzjsnnwtQ22gngVpwww3SunW5scZG6T/+I518gAwKoEBbxRUMx41LPo/2oAAKpGmRpN2zng9SdOrepyXdJEnu/oikbpL65Z/I3a9w9/HuPr5///5lSheA5s4Nj3ynn558LkDto50Eqt369dJ110XjU6ZIAwcmnw+QhQIo0FbPPReNVUsBNC7PuJ8HQDk8LmlPMxtqZl0UNm+YmveaNyQdI0lmNlrhxo6hK0Ba4kZ/jh4t7bVX8rkAtY92Eqh2N94YpsBna2yUzjknnXyALBRAgbbYskWaPz8ar5YCaNwN22uvRReoBlBy7r5V0nmS7pI0T2EX2+fN7Ptm1ryV9AWSPmNmz0i6XtLZ7p4//Q9AElatCut/5jvtNMniZuoC6AjaSaDKbdwYP/rzpJMY/YmK0CntBICq8tJLYTfYbDvvLL3nPenk01a9eklDhoSiZ7bnn5cmTkwjI6CuuPs0hU0bsmPfzvp+rqRDk84LQIypU6Ntfq9e0vHHp5MPUAdoJ4EqduutofMwW0MDoz9RMRgBCrRF3HqZY8dW10iQuNGqrAMKAMB2TU3SLbdE4yefLHXtmnw+AABUss2b43d+nzRJ2m235PMBYlAABdqimjdAasY6oAAAtGzWLGlJ3t4rZtKpp6aTDwAAlezOO6Vly3JjZoz+REWhAAq0RS0UQON2gn/uuTDaBQAASLfdFo0dcgijWAAAyNfUJP35z9H4UUdJQ4cmnw9QAAVQoFgrV0qLF+fGGhqkMWPSyae9hg+XunfPja1ZIy1cmE4+AABUknfekR54IBr/8IeTzwUAgEo3c6b0+uvR+NlnJ54K0BIKoECx4qaJDxsm9eiRfC4d0dgojR4djbMOKAAA0rRp0tatubG+faVD2XcFAICIa6+NxiZMqL6BQqh5ZSuAmtnVZrbMzJ7Liu1sZneb2UuZr33KdX2g5OIKoNU2/b0ZGyEBABDlHj/9/cQTQwciAADYbs6c8Mj3yU8mnwvQinKOAP2TpEl5sQsl3evue0q6N/McqA61sP5nMwqgAABEPfus9Oqr0fjJJyefCwAAlS5u9OeIEdJBByWfC9CKshVA3f0BSSvzwidLal4d98+SPliu6wMl1dQkPf98NB63oVA1iMv75ZeljRuTzwUAgEpx++3R2H77SYMHJ58LAACVbOFCacaMaPzjHw87wAMVJuk1QHdx96WSlPk6IOHrA+3z6qvShg25sZ49pSFDUkmnw/r1k97zntxYU5M0b146+QAAkLYNG6S7747GGf0JAEDU9deHpWOyDRggHXtsOvkArajYTZDM7Fwzm21ms5cvX552Oqh3caM/99or7AJfreKmwc+dm3weAABUgnvuiXZ29ughHXNMOvkAAFCp1qyR7rgjGj/zTKlTp+TzAYqQdPXmLTN7jyRlvi4r9EJ3v8Ldx7v7+P79+yeWIBArrjBYrdPfm8XtykcBFABQr6ZOjcYmTZK6d08+FwAAKtntt0eXT+vRQ/ogqxyiciVdAJ0qqXk7sE9KilloCahAcYXB0aOTz6OU4gqgcSNdAQCodUuWSE8/HY0z/R0AgFzbtkk33hiNn3SStOOOyecDFKlsBVAzu17SI5JGmtkiM/u0pJ9KOtbMXpJ0bOY5UNk2b5ZefDEa32uv5HMppVGjootTL14srV6dTj4AAKRl2rRobOjQ+M5CAADq2cyZ0ptv5sbMpI98JJ18gCKVbXEGdz+zwCEWUkJ1efllaevW3FjfvlK1L83Qo0e4uVuwIDc+d640cWI6OQEAkDT3+ALoCSewiy0AAPluuCEae9/7pN13Tz4XoA2qeAcXICFx09/32qs2bopYBxQAUO/mzpXeeCManzw5+VwAAKhkL74oPflkNM7oT1QBCqBAa+IKgrUyJY51QAEA9e4f/4jGDjhA2nXX5HMBAKCS3XRTNDZsmDRhQvK5AG1EARRoTVxBsFYKoHHrmDICFABQL7ZulaZPj8ZPOCH5XAAAqGRr1kj//Gc0fsYZtTE7EjWPAijQko0bpVdfjcZrpQC6555SY2NubMUKafnydPIBACBJ//qXtGpVbqxLF+kYlqwHACDHHXdImzblxnbYgU5DVA0KoEBL5s+XmppyYwMHSr17p5NPqXXpEoqg+RgFCgCoB3EjWY44ItzQAQCAoKlJuvnmaHzKFKl79+TzAdqBAijQklpe/7MZ64ACAOrRunXSzJnROCNZAADI9eij0qJF0fippyafC9BOFECBltRDAZR1QAEA9WjGDGnz5txY797SxImppAMAQMW65ZZo7OCDpcGDk88FaCcKoEBL4gqBcQXDahZX0J07V3JPPhcAAJISt/nRccdJnTolnwsAAJXqrbekBx+Mxk87LflcgA6gAAoUsmaNtHBhbsxMGjUqnXzKZdgwqWvX3NiaNdLixenkAwBAua1aJc2aFY1PmpR8LgAAVLLbbovui7HLLtJhh6WTD9BOFECBQubNi8b22EPq2TP5XMqpsVEaOTIaZxo8AKBW3Xdf/M3c2LHp5AMAQCXaulW69dZo/EMfCveRQBWhAAoUErcRUK2t/9ksblo/GyEBAGpVoenvDfzTGACAf3vwQWnFitxYQ4N08snp5AN0AP/KAwqJGwFaa+t/Nosr7Mb9/AAAVLsVK6QnnojGjzsu+VwAAKhkcaM/jzxS6tcv8VSAjqIAChQSVwAcPTr5PJIQV9idPz86PRCAzGy2mX3BzPqknQuAdrjnnuhGf7vvXntrfAMpoZ0EasSSJdIjj0TjH/5w8rkAJUABFIjzzjvSm2/mxhoa4tfKrAWDBkk9euTGNmyQ3ngjnXyAyvYRSQMlPW5mN5jZ8WZmaScFoEhx09+PPTZsdAigFGgngVpw++3RDsOBA6UJE9LJB+ggCqBAnLjRn3G7pdeKhob4kS9Mgwci3P1ld/+mpBGSrpN0taQ3zOx7ZrZzutkBaNHSpdKcOdH48ccnnwtQo2gngRqwbZs0dWo0fsoprJeNqsVvLhBn/vxorFanvzeL+/kogAKxzGxvSb+U9AtJ/yfpVElrJN2XZl4AWnH33dHYsGHS8OHJ5wLUMNpJoMo9/LC0fHlurLFRmjIlnXyAEuiUdgJARaqn9T+bxW2EFFcIBuqcmT0haZWkP0i60N03ZQ49amaHppcZgFbdc080xuhPoKRoJ4EacNtt0djhh0t9+yafC1AiFECBOPVYAI37+Zo3QmKaA5DtNHdfkB0ws6Hu/qq7fyitpAC0YskSae7caPzYY5PPBahttJNANVu2THrooWj8lFOSzwUoIaoaQL5CGyCNGJFOPkkptBHSwoXp5ANUrluKjAGoJPfFzLwdMUIaPDj5XIDaRjsJVLO//z0Mgsm2yy7SwQenkw9QIowABfLV2wZIzZo3Qnryydz43LnSHnukkxNQQcxslKS9JO1kZtkjWHpJ6pZOVgCKdu+90dgxxySfB1CjaCeBGtDUFL/50ZQpzApE1aMACuSrxw2Qmo0eHS2AzpsnTZ6cTj5AZRkp6URJvSWdlBVfK+kzqWQEoDjLlknPPhuNUwAFSol2Eqh2Tz0lLVqUGzOTTjop/vVAFaEACuSrx/U/m7ERElCQu98u6XYzm+juj6SdD4A2iJv+PmyYNGRI4qkAtYp2EqgBt98ejU2YIA0cmHwuQIlRAAXyxRVAR41KPo80sBESUJCZfd3dfy7po2Z2Zv5xd/9SCmkBKAbT34Gyo50Eqty6dfHt5Qc/mHwuQBlQAAWyrVpVnxsgNWveCGnDhu2x5o2QWAcUaO4dmZ1qFgDaZsUK6emno3EKoECp0U4C1ezuu6VNm3JjvXpJRx6ZSjpAqVEABbIV2gCpW52s215oI6R58yiAou65+x2Zr39OOxcAbXD//ZJ7bmzwYGn48HTyAWoU7SRQ5eI2P5o0SerSJflcgDKgAApkq+f1P5uNGRO/E/ykSenkA1QIM7tDkhc67u5TEkwHQLHipvO9//1hUwcAJUM7CVSx116L3yxwCv/bonZQAAWyUQAtvA4ogIvTTgBAG73zTrRTT5KOPjr5XIDaRzsJVKs77ojG9txTGjky+VyAMqEACmSr5w2QmrEREhDL3WemnQOANpo5M7Rf2QYO5IYOKAPaSaBKNTVJ06ZF4yedxGwJ1BQKoECzet8AqRkbIQGxzOwmdz/dzJ5V7hQ/k+TuvndKqQEo5P77o7FjjuGGDigD2kmgSs2aJS1fnhtrbJQmT04nH6BMKIACzeJGfw4dWj8bIDVjIySgkP/KfD0x1SwAFGf9eumxx6Lxo45KPhegPtBOAtXo73+Pxg47TOrTJ/lcgDJiPivQjPU/t4v7ueM+H6COuPvSzNfXJW2StI+kvSVtysQAVJKHH5a2bMmN9e0rjR2bTj5AjaOdBKrQ2rXSjBnR+EknJZ4KUG4UQIFmcRv9UADdjgIoIEkys/+Q9JikD0k6VdIsM/tUulkBiIi7oTviCNazBsqMdhKoInffLW3enBvr3Vs69NB08gHKiCnwQDNGgG4X93O/8AIbIQHB1yTt5+5vS5KZ9ZX0L0lXp5oVgO02b5YeeigaZ/o7kATaSaBaxE1/nzRJ6tw5+VyAMqOSAUjS6tXS0qW5sYYGac8908knbbvvHjZCyrZ+vbRoUTr5AJVlkaS1Wc/XSlqYUi4A4syenbuZnyTtsIM0fnw6+QD1hXYSqAYLF0pz5kTjJ7KML2pTKiNAzewrkv5DYXfAZyWd4+7vppELICl++vuQIVL37omnUhEaGqSRI6WnnsqNz58vDR6cTk5Ayszs/My3iyU9ama3K7RjJytM9QNQKeJ2fz/sMEa0AGVEOwlUmX/8IxobPjzcBwI1KPERoGa2m6QvSRrv7mMlNUr6SNJ5ADnipr+PGpV8HpWEdUCBfDtmHq9Iuk3hpk6Sbpe0tNCbspnZJDN7wcxeNrMLC7zmdDOba2bPm9l1pUgcqCtNTdLMmdH4kUcmngpQZ2gngWrR1CRNmxaNn3iiZJZ8PkAC0loDtJOk7ma2RVIPSUtSygMIWP8zKq4AHDdSFqgT7v69jrzfzBol/VbSsQrTAx83s6nuPjfrNXtK+m9Jh7r7O2Y2oCPXBOrSnDnSypW5sS5dpEMOSScfoE7QTgJV5OmnpSV5ZZiGhrD+J1CjEi+AuvtiM7tY0huSNkqa7u7Tk84DyEEBNCru558/X3KnVxB1zcz6S/q6pL0kdWuOu/vRrbz1QEkvu/uCzHluUJgWODfrNZ+R9Ft3fydzzmUlTB2oD3HT3w86KLq2NYCyoJ0EqkDc9PcDD5T6908+FyAhaUyB76PQkA2VNFBSTzM7K+Z155rZbDObvXz58qTTRD1Zsyba+2UmjRiRTj6VYo89omugrl0rLV6cTj5A5firpPkK7dj3JL0m6fEi3rebcjeBWJSJZRshaYSZPWxms8yMbnigLdylGTOicXZ/B5JEOwlUsk2bpHvuicbZ/Ag1Lo1d4N8v6VV3X+7uWyT9TVJkTpK7X+Hu4919fH96IVBOcdO699iDkSINDfFFYNYBBfq6+x8kbXH3me7+KUkHF/G+uKHTnve8k6Q9JR0p6UxJV5lZ78iJ6CQE4r36arSjrqFBet/70skHqE+0k0AlmzlTWr8+N9ajB2tlo+alUQB9Q9LBZtbDzEzSMZKoqCA9cQXQep/+3oyNkIA4WzJfl5rZB8xsP0mDinjfIkm7Zz0fpOga2Isk3e7uW9z9VUkvKNzo5aCTECggbvTnPvtIffokngpQx2gngUr2z39GY0cfLXXrFo0DNSTxAqi7PyrpFklPSno2k8MVSecB/BvrfxZWaB1QoL790Mx2knSBpK9KukrSV4p43+OS9jSzoWbWRdJHJE3Ne81tko6SJDPrpzDVb0GpEgdqXtzu70cckXweQH2jnQQq1TvvSP/6VzT+gQ8knwuQsFR2gXf370j6ThrXBiLiCqBxO6DXIzZCAiLc/e+Zb1crcxNW5Pu2mtl5ku6S1Cjpand/3sy+L2m2u0/NHDvOzOZK2ibpa+7+dml/AqBGLV8uPf98NH744cnnAtQx2kmggk2fLm3blhsbMEA64IB08gESlEoBFKgYa9dKixZF4yNHJp9LJdpjD6lr17BQdrM1a6SlS6WBA9PLC0iRmQ2TdKmkiZKaJD0i6SvNu9a2xN2nSZqWF/t21vcu6fzMA0BbPPhgNDZ0qDR4cPK5AHWMdhKoYNOmRWOTJoX1soEax2856tsLL0RjgwdLPXsmn0slamyMLwazDijq23WSbpK0q6SBkm6WdH2qGQFg+jtQOWgngUr0xhvxMyWY/o46QQEU9Y31P1sXtxwA64Civpm7X+vuWzOPvyi6Sy2AJG3YID3+eDROARRIA+0kUIniRn+OGCENH558LkAKmAKP+kYBtHXsBA9Iksxs58y395vZhZJuULihO0PSP1JLDIA0a5a0eXNurG9faa+90skHqEO0k0AFc4/f/X3y5ORzAVJCART1LW4kIxsg5Yr7PObNYyMk1KMnFG7kmn/xP5t1zCX9IPGMAAQzZkRjhx/OmmZAsmgngUr17LPS4sW5MbOw/idQJyiAon6tWxfWQclHATTXsGFSly65I2tWr2YjJNQddx+adg4AYmzbJj30UDTO9HcgUbSTQAWLG/05YYLUv3/yuQApoVsc9Stu9OfgwdIOOySfSyUrtBES64CiTplZZzP7kpndknmcZ2ad084LqFvPPCOtWZMb69Yt3NgBSBztJFBhtm6Vpk+Pxk84IflcgBRRAEX9Yv3P4sV9LnPnJp8HUBkuk3SApN9lHgdkYgDSELf7+8SJUteuyecCQKKdBCrLI4+EGXzZunaVjjoqnXyAlBQ1Bd7M/k/S1ZL+6e5N5U0JSAgF0OKxERKQbYK775P1/D4zeya1bIB65i498EA0fvjhyecCoBntJFBJ4qa/H3GE1LNn8rkAKSp2BOhlkj4q6SUz+6mZsUgiqh8F0OIVKoC6J58LkL5tZja8+YmZDZO0LcV8gPr1+uvSwoW5MTPpsMPSyQeARDsJVI4NG+JnSrD5EepQUSNA3f0eSfeY2U6SzpR0t5ktlHSlpL+4+5Yy5giU3tq10RsmiQ2QChk6NEyT2LRpe2zNGjZCQr36mqT7zWyBwk63e0g6J92UgDoVN/pz772lPn2SzwVAM9pJoFLcf3/uPZwk7bSTdMgh6eQDpKjoXeDNrK+ksyR9XNJTkv4q6TBJn5R0ZDmSA8qm0AZITAOI17wR0pw5ufF58yiAoq6YWYOkjZL2lDRS4cZuvrtvavGNAMqD6e9ARaGdBCrMtGnR2LHHSp2KLgUBNaOoKfBm9jdJD0rqIekkd5/i7je6+xclsWU2qk/c9PcxY5LPo5rEjY5lHVDUmcw62L90903uPsfdn+GmDkjJqlXRjjmJAiiQItpJoIK8/bb0+OPR+OTJyecCVIBi1wC9yt3HuPtP3H2pJJlZV0ly9/Flyw4ol7gRoKz/2TJ2ggeaTTezD5uZpZ0IUNceflhqytubc9AgaciQVNIB8G+0k0AlmD492k4OHBiWigHqULHjnn8oKX/s9COS9i9tOkBC4gp3FEBbFjdCdv78sBES/75FfTlfUk9JW83sXYXpfe7uvdJNC6gzcZs6HH44bRKQPtpJoBLE7f4+aRLtJOpWiwVQM9tV0m6SupvZfgqNlyT1UpgOD1SftWulRYtyY2ZhjUsUNmRI/EZIS5ZIu+2WWlpA0tx9x7RzAOre5s3SrFnR+BFHJJ8LgBy0k0AFeOON+EE/7P6OOtbaCNDjJZ0taZCkS7LiayVdVKacgPJiA6T2aWkjJAqgqANmNkCh7XuvpDmSfurua9LNCqhTTzwhbdiQG9txR2mffdLJBwDtJFBJ7rwzGhsxQho2LPlcgArR4hqg7v5ndz9K0tnuflTWY4q7/y2hHIHSYgOk9otbJoCNkFA/rpG0XtKvJe0o6VfppgPUsbjd3w89lF1tgXTRTgKVwD2+AMroT9S51qbAn+Xuf5E0xMzOzz/u7pfEvA2obHEFO9b/LA4FUNS3Xd39m5nv7zKzJ1PNBqhX7vEFUHZ/B9JGOwlUgnnzwhT4bGYUQFH3Wusmb54TvEO5EwESE1ewGzUq+TyqUaECKBshoT6YmfXR9vWwG7Ofu/vK1DID6slLL0lvvZUba2yUJk5MJx8AzWgngUoQt/nR/vtLAwYknwtQQVosgLr77zNfv5dMOkCZrVkTvwESBdDiDBkidesmvfvu9tjatdLixdKgQamlBSRkJ0lPaPuNnSQ1j25xSSyqBCQhbvTn/vuHNUABpIl2EkhbU5N0113ROKM/gVZHgEqSzOznkn4oaaOkOyXtI+nLmenxQPWI2wBpjz2kHj2Sz6UaNTaGxbPzN0KaO5cCKGqeuw9JOwcAii+Avu99yecBIAftJFABZs+WVuYNtu7cWTrmmHTyASpIi5sgZTkus4PfiZIWSRoh6Wtlywool+efj8bYAKlt4j6vuXOTzwMAUH9WrIhvc1j/EwCA+Onvhx4q9eqVfC5AhSm2ANo58/UESdezfguqVtxNEwXQtqEACgBIy0MPRWPDhjELAQCATZuke++Nxpn+DkgqvgB6h5nNlzRe0r1m1l/Su628B6g8jADtuL32isbmzQvrzQAAUE5MfwcAIN5DD0kbNuTGevSgnQQyiiqAuvuFkiZKGu/uWyStl3RyORMDSu7tt6Vly3JjjY3SyJHp5FOtdt9d6tkzN7Zxo/Taa6mkA6TBzA4zs3My3/c3s6Fp5wTUvE2bpEcfjcaZ/g5UHNpJIAV33hmNHX201LVr8rkAFaioTZAyRksaYmbZ77mmxPkA5RM3TXv4cBqEtmpoCKNmH388Nz53bpiGCNQ4M/uOwoyIkZL+qLBMzF8kHZpmXkDNe+yxUATN1ru3NG5cOvkAiEU7CaRgzZr4ZWImT04+F6BCFTUC1MyulXSxpMMkTcg8xpcxL6D04gqgcdO50TrWAUV9O0XSFIXZEHL3JZJ2TDUjoB48+GA0dthhoWMOQCWhnQSSdt990pYtubGdd5YmTEgnH6ACFTsCdLykMe7u5UwGKCvW/yyduMJx3OcL1KbN7u5m5pJkZj1bewOADmpqii+AMv0dqES0k0DS4qa/H388nYRAlmL/b3hO0q7lTAQoK3dGgJZSXOH4xRejvY5AbbrJzH4vqbeZfUbSPZKuTDknoLbNny8tX54b69xZOvjgdPIB0BLaSSBJy5ZJTzwRjbP7O5Cj2BGg/STNNbPHJP178SV3n1KWrIBSW7pUWrUqN9alC2tWttcuu4QpFStXbo9t2SK9/LI0enR6eQEJcPeLzexYSWsU1jf7trvfnXJaQG2LG/15wAFhd1sAFYV2EkjY9OlhwE+23XdntiOQp9gC6HfLmQRQdnGjP0eOlDq1ZR8w/JtZKHQ+/HBufO5cCqCoeWb2FUk3czMHJGjmzGiM6e9ARaKdBBL2z39GY5Mnh3s2AP9W1BR4d58p6TVJnTPfPy7pyTLmBZRWXAGUHrGOYR1Q1K9eku4yswfN7AtmtkvaCQE17c03wzIr+SiAApWKdhJIyquvSi+8EI0z/R2IKHYX+M9IukXS7zOh3STdVq6kgJKLK8yx/mfHsBM86pS7f8/d95L0BUkDJc00s3tSTguoXXHT30eMkHZleXqgEtFOAgmKG/05Zow0eHDyuQAVrthNkL4g6VCFdVzk7i9JGlCupICSamqS5s2LxhkB2jFxn9+CBdLGjcnnAqRjmaQ3Jb0t2kSgfB54IBpj9CdQDWgngXJyj9/9ndGfQKxiC6Cb3H1z8xMz6yTJW3h9i8yst5ndYmbzzWyemU1s77mAVr3+urRhQ26sZ096xTpq552jo2+amuKnYAA1xMz+08xmSLpXYZPAz7j73ulmBdSoDRuk2bOjcQqgQMWinQQS8uyz0pIlubGGBum449LJB6hwxe4AM9PMLpLUPbOj3+cl3dGB614q6U53P9XMukhiC0+UT9y07NGjQ+OAjhkzJqzNlm3uXGnffdPJB0jGHpK+7O5Pp50IUPNmzZK2bMmN9esnjRqVTj4AikE7CSQhbvr7hAmhnQQQUWwF6EJJyyU9K+mzkqZJ+lZ7LmhmvSQdLukPkuTum919TS4VTQAAIABJREFUVXvOBRQlbv1Ppr+XBhshoY5k2i9J+rmkN8xs5+xHmrkBNavQ7u90YgIVh3YSSNDWrdLdd0fjkycnnwtQJYoaAeruTWZ2m6Tb3H15B685TKGY+kcz20fSE5L+y93XZ7/IzM6VdK4kDWaqMjqCDZDKJ66QTAEUtes6SScqtFsuybKOuUL7BqBUmpqkhx6Kxpn+DlQq2kkgKbNmSavyxpF16SIddVQ6+QBVoMXucwu+a2YrJM2X9IKZLTezb3fgmp0k7S/pMnffT9J6hRGmOdz9Cncf7+7j+/fv34HLoa5t3hy/JuXYscnnUovGjJHMcmOLFkUbY6AGuPuJma9D3X1Y5mvzg5s6oNTmzJFWr86Nde0apvcBqDi0k0CCpk2Lxo44Iux1ASBWa/OHvqyw+/sEd+/r7jtLOkjSoWb2lXZec5GkRe7+aOb5LQoFUaD0XnghTA/I1q+fNICNKEuiZ09p6NBo/Lnnks8FSIiZ3VtMDEAHxe3+fvDBoQgKoGLRTgJltmFD/BIxTH8HWtRaAfQTks5091ebA+6+QNJZmWNt5u5vSlpoZiMzoWMkxexSA5TAs89GY+PGRUctov3GjYvGKICiBplZt8waZv3MrE/WumZDJA1MNzugBsXd3B1xRPJ5ACgK7SSQkBkzpE2bcmO9ekkTJ6aSDlAtWlsDtLO7r8gPuvtyM+vcget+UdJfMzvAL5B0TgfOBRQWV4hj+ntpjR0r3X57biyu8AxUv88qzIwYqLC+WXNPyhpJv00rKaAmvf56eGQzkw47LJ18ABSDdhJIQtz092OPlTp3pEQD1L7WCqCb23msRe7+tKTx7X0/ULS4AmjciEW0X9zn+fzzYfMKdulFDXH3SyVdamZfdPdfp50PUNPiRn+OGyftzEbSQKWinQQSsGKF9Nhj0fgJJySfC1BlWiuA7mNma2LiJqlbGfIBSmflSmnJktxYQ4M0alQ6+dSqYcOkHj3CWjTN1q0LI3fi1gcFqpy7/9rMxkoao6y20N2vSS8roMbMmBGNMf0dqAq0k0AZTZ8eBppkGzhQ2nvvdPIBqkiLBVB3b0wqEaDk4kZ/vve9oViH0mloCLvBz56dG3/uOQqgqElm9h1JRyrc2E2TNFnSQ5K4sQNKYeXK+KVUKIACVYF2EiijuOnvkyaxxwVQBOanonax/mdy4j5X1gFF7TpVYQO/N939HEn7SGJbaqBUHnxQcs+NDR4sDRmSSjoA2ox2EiiHBQuk+fOjcXZ/B4pCARS1K64ARwG0PNgJHvVlo7s3SdpqZr2k/2/vzuOkqs78j3+f7qZZhAZRUFFaZRQVF0TANaCgIEaWmGDUiInRxDETY/yZTNaZTCaZ7DNJJhNNNCZjNE5wQ0QElygioqKoCAqigCaSViAiizR7nd8fpztU1b3dVHdX3Vv31uf9et1XVz/3VvOcqqaerlNn0VpJA2LOCUgPdn8Hko46CZTC7NnB2DHHMOsOKNDe1gAFkimT8Rvx5KMDtDTCHtcVK6StW6WuXaPPByithWbWS9Jv5He5/UBSyGr0ANps2zZpwYJgnA5QIEmok0CxZTLhHaBsfgQUjA5QpNObb+ZuyiNJ++zD9LlS2W8/6aCDpHfe2RPLZKRly6STToovL6AEnHP/1HTz12b2kKQ659ziOHMCUmPBAmn79tzYvvuyuQOQINRJoAReekl6993cWFWVdO658eQDJBBT4JFOLU1/r+JXvmSYBo+UM7OT8g9JvSXVNN0u5GeMM7PlZrbCzL7WynWTzcyZ2bBi5Q8kQtj09xEjqN9AAlAngRJ68MFg7NRTpd69o88FSChGgCKd2AApescdJz3ySG6MDlCky3+1cs5JGt3anc2sWtINksZIWi3peTOb4ZxbmnddD0nXSgqZBwykWCbjN0DKx/R3ICmok0ApbN8uPfZYMH7++dHnAiQYHaBIp7ARoGEjFFE87ASPlHPOjergjzhZ0grn3CpJMrOpkiZJWpp33Xcl/VjSlzv47wHJsnix9P77ubHaWumUU+LJB0CbUCeBEpk7V9qyJTfWrRsfEAJtRAco0qexUVq1Khg/9tjoc6kkRx8t1dRIu3btia1bJ61dK/XtG19eQJGZ2SfD4s652/Zy14MlvZ31/WpJOT07ZjZEUn/n3Ewza/GNnZldJekqSaqvry8kbaD8zZkTjJ16qtSlS/S5AGg36iRQZGHT388+m/oItBELKiF9XnlFci43dsghfhMFlE5trTRwYDD+8svR5wKU1vCsY4Skb0uaWMD9LCT29xcrM6uS9DNJX9rbD3LO3eycG+acG9anT59CcgbKm3PhHaBnnRV5KgA6jDoJFMv69dIzzwTjTH8H2owRoEifRYuCMaa/R+P446WlebOUXn5ZGjMmnnyAEnDOfSH7ezPrKen2Au66WlL/rO8PkdSQ9X0PScdJesLMJOlASTPMbKJzbmGHkgbK3YoVUkNDbqyqym+ABCBRqJNAET30kF8jO9sBB0gnFbSvGIAsjABF+oSNOBw8OPo8KlHY48wIUKRfo6QjC7jueUlHmtnhZlYr6WJJM5pPOuc2Ouf2d84d5pw7TNKzknhTh8oQNvrzxBOZvQGkA3USaK+ZM4Ox88/3HxICaBNGgCJdMpnwjXdOPDH6XCpR2OO8fLlfl7Vbt+jzAUrAzB7Qnil5VZIGSbprb/dzzu0ys2skPSypWtLvnHOvmtl3JC10zs1o/ScAKfbEE8HYqI7upwIgDtRJoEjeeEN6/fVg/MMfjj4XIAXoAEW6rFjhO9uyde8uDRgQTz6Vpm9f6aCDpHfe2RPLZKRXX5WGD48vL6C4/jPr9i5Jf3bOrS7kjs65WZJm5cW+1cK1Z7U3QSBRGhrC3+Cx/ieQVNRJoBjCRn8OGiQddljkqQBpQAco0iVs/c8TTmCKQJQGD87tAJX8NHg6QJESzrm5kmRmdWqqo2bW2zm3PtbEgKQKm/5+9NH+AzUAiUOdBIpg925p9uxgfPz46HMBUoJeIaQL63/GL+zxDuuYBhLKzK4yszWSFktaKOmFpq8A2iOsA5Tp70BiUSeBInjmGb8DfLaaGuncc+PJB0gBRoAiXegAjV/Y4714sZ8Kz0hcpMM/SzrWOfe3uBMBEm/9+vDaTQcokGTUSaCjwqa/jxwp9ewZfS5AStAbgfRYu1Z6993cWFWVdOyx8eRTqY44Qtpnn9xYY6NfnxVIh5XyO9oC6Kgnn5Scy43V10uHHx5PPgCKgToJdMSmTdLcucE409+BDmEEKNIjbJr10UdLXbtGn0slq6qSjj9eevbZ3PjLL0sDB8aTE1BcX5f0tJktkLS9Oeicuza+lICECpv+ftZZklnkqQAoGuok0BEPPyzt3Jkb691bOv30ePIBUoIOUKRHWAco09/jMXhweAfohRfGkw9QXDdJelzSEkmZmHMBkmvzZmnBgmCc3d+BpKNOAh3xwAPB2Lhxfg1QAO3G/yCkR9gaYieeGH0eCH/cw54fIJl2OeeujzsJIPHmzZN27cqN9ekjHXdcPPkAKBbqJNBeK1dKS5cG4xMnRp8LkDKsAYp0aGyU3ngjGGcEaDyOOy644dE77/h1WoHkm9O0w+1BZta7+Yg7KSBx/vSnYGz0aDbMA5KPOgm014wZwdgxx/h9FgB0CCNAkQ6vvOJ3Gc/Wr5+0//7x5FPpunaVjjpKWrYsN75okTR2bDw5AcXziaavX8+KOUkDYsgFSKbGxuBSKZJ09tnR5wKg2KiTQHvs3CnNmhWMT5gQfS5ACtEBinQIW/+T6e/xGjw42AH68st0gCLxnHNsTw101FNPSTt25MZ696Z2AylAnQTa6amnpPffz4116uTX/wTQYXSAIh3YAKn8DB4sTZ2aG3vppXhyAYrIzD4ZFnfO3RZ1LkBihU1/HzWK6e9AClAngXa6//5gbNQoqa4u+lyAFKIDFMm3cycbIJWjsMf/jTekTZso4ki64Vm3u0g6W9KLknhjBxRi61Zp/vxgnOnvQFpQJ4G2WrdOevrpYJzp70DR0AGK5Fu6VNq+PTfWq5d0OLNvYtWnj1RfL/3lL3tizvnRuiNHxpcX0EHOuS9kf29mPSXdHlM6QPI8/XSwbvfsKQ0dGk8+AIqKOgm0w8yZwT0tDjhAOuWUePIBUoh5Rki+F14Ixk46iWl05WDYsGBs4cLo8wBKq1HSkXEnASTGY48FY2edJVVXR54KgEhQJ4HWZDLh098nTuQ9LVBEjABF8oV1qIV1vCF6Q4dK06blxsI6rIEEMbMH5HezlfwHiYMk3RVfRkCCbN/uN3nIx/R3IDWok0AbvfSStHp1MM70d6Co6ABFsrW0/ifT6MrDSScFY6+/zjqgSLr/zLq9S9KfnXMhf7UCCHj6aamxMTfWo4c0fHj49QCSiDoJtMV99wVjp5wi9esXfS5AitEBimRj/c/yxjqgSBEzO0LSAc65uXnxEWbW2Tm3MqbUgOR45JFgbORIqVOn6HMBUFTUSaAdNm2SHn88GP/IR6LPBUg5FpRAsrH+Z/ljHVCkx88lbQ6Jb206B6A1W7dK8+YF4+eeG30uAEqBOgm01YMPSjt25MZ69pTOPDOefIAUo5cIycb6n+UvbDkC1gFFMh3mnFucH3TOLZR0WPTpAAkzb560bVturK5OOvnkePIBUGzUSaAtnAuf/j5+vFRbG30+QMrF1gFqZtVm9pKZzYwrByQc638mQ2vrgALJ0qWVc10jywJIqocfDsbOPluqYUUmICWok0BbLF4srVoVjDP9HSiJOEeAflHSshj/fSQd638mQ/M6oNma1wEFkuV5M/tsftDMrpTEsGagNZs3+w2Q8o0dG30uAEqFOgm0xb33BmMnnsj7WaBEYvnI3cwOkXS+pO9Juj6OHJACrP+ZHMOG5W6EJPnlC9gICclynaT7zOxS7XkjN0xSraQLYssKSIInnvAzN7L17s2sDSBdqJNAoTZtkv70p2D8ox+NPhegQsQ15+jnkr4iqUdM/z7SgPU/k2PoUGnatNwY64AiYZxzaySdbmajJB3XFH7QOReydSeAHI8+GoyNGcOHlkCKUCeBNpg5M7j5UV2ddM458eQDVIDIO0DNbLyktc65F8zsrFauu0rSVZJUnz99FmD9z2RpbR3Qurro8wE6wDk3R9KcuPMAEmPDBunZZ4Nxdn8HUok6CeyFc9I99wTjbH4ElFQcH7ufIWmimb0laaqk0Wb2h/yLnHM3O+eGOeeG9enTJ+ocUe6WLGH9zyRpaR3QsFG8AIB0efxxKZPJjR1wgHTcceHXAwCQZgsXBpcHk6TJk6PPBaggkXeAOue+7pw7xDl3mKSLJT3unJsSdR5IuLCRJEOHMpWunIUtT7BgQfR5AACi9dBDwdjYsdRsAEBluvvuYGz48OCAEQBFxV+eSKawDtBTT40+DxQu7Pl55hk/EhQAkE7vvCO9+GIwPmZM9LkAABC3tWv9xoD5Lrww8lSAShNrB6hz7gnn3Pg4c0ACbdggLVsWjNMBWt6GDw+O9mlokFavjicfAEDpzZ4djNXXS8ccE30uAADEbfr04LIwffpII0fGkw9QQRgBiuR57rngqMFDD5UOOiiefFCYHj3C13sLG80LAEg+56RZs4Lx88+XzKLPBwCAOO3cKd17bzB+wQVSTeT7UwMVhw5QJA/T35OrpWnwAID0ee016a23gvHzzos8FQAAYjdnjvTee7mx6mrfAQqg5OgARbI4RwdokoU9TwsXSrt2RZ8LAKC0wkZ/Dhki9esXfS4AAMRt6tRgbPRoPwUeQMnRAYpkefNNv3B0tpoavwM8yt+xx0rdu+fGGhulJUviyQcAUBq7d0sPPxyMM/oTAFCJli2TFi8Oxtn8CIgMHaBIlrDRn4MHS926RZ8L2q66Wjr55GCcdUABIF2efVZavz431qmTdM458eQDAECc7rwzGBs40M+MABAJOkCRLEx/Tz7WAQWA9HvwwWBsxAipri76XAAAiNP69eGzIi66iE0BgQjRAYrk2LFDeuGFYPy006LPBe0X1gG6bJm0cWP0uQAAim/LFumJJ4Lx88+PPBUAAGJ3zz1+B/hsdXXSuHHx5ANUKDpAkRyLFknbt+fGevXyUweQHP36SfX1uTHnpOeeiycfAEBxPfqo/9AyW12ddPrp8eQDAEBcduzwHaD5PvYxqXPn6PMBKhgdoEiOsOnvp5wiVfFrnDhMgweA9Lr//mBs7Fi/BigAAJXkoYeCa2JXV7P5ERADeo6QHE89FYwx/T2ZwjpA58+XMpnocwEAFM+qVdKSJcH4pEnR5wIAQJyck+64Ixg/+2ypb9/o8wEqHB2gSIa33/ZvqvKxAVIyDRsWHAn03nvS0qXx5AMAKI7p04OxgQOlo4+OPhcAAOK0YIG0cmUwPmVK9LkAoAMUCfHkk8HYccdJ++8ffS7ouG7dpOHDg/Gw5xkAkAw7d0qzZgXjkyaxyy0AoPLcdlswNmSINGhQ9LkAoAMUCTF3bjA2cmT0eaB4zjwzGAt7ngEAyfDkk9KGDbmx2lrpvPPiyQcAgLgsXx6+yeull0afCwBJdIAiCTZu9DvA5wvrQENyjBgRjK1cKf31r9HnAgDouLDNj846y+8ADwBAJbn99mCsvp5BPECM6ABF+QvbHOfgg6UBA+LJB8XRt2/49A9GgQJA8qxZIz3zTDD+kY9EnwsAAHFqaJAeeSQYnzJFqqILBogL//tQ/sI6xM48k/XE0iDsE1DWAQWA5HngAb/bbbZ+/fymdwAAVJI//CE4gKd3b2n8+HjyASCJDlCUux07wkeUMHUgHcKexxdflDZtij4XAED77N4t3XdfMD5xIiNdAACVZf16afr0YPySS/y62ABiw1+lKG8LF0qNjbmxHj2kE0+MJx8U15FHSgcdlBvLZPyyBwCAZJg3z0+Bz1ZVJU2YEE8+AADE5Y47/CCebN26SZMnx5MPgL+jAxTlLWw69Ic+JNXURJ8Lis+MafAAkHR33RWMjRghHXBA9LkAABCXTZuku+8OxidP9oN4AMSKDlCUL+fCO8KY/p4uZ54ZjM2fL+3cGX0uAIC2eest6bnngvGPfzzyVAAAiNWddwZnL9bWSpdeGk8+AHLQAYrytXSptHZtbqymRjrttHjyQWkMGSLts09urLEx/A01kHBmNs7MlpvZCjP7Wsj5681sqZktNrPHzOzQOPIEChY20qW+Xho+PPpcACQedRKJtWWL9H//F4xPmiTtt1/0+QAIoAMU5evhh4OxoUOl7t2jzwWl06mTdMYZwfgjj0SfC1BCZlYt6QZJ50kaJOkSMxuUd9lLkoY5506QdI+kH0ebJdAGjY3SzJnB+IUXsvkRgDajTiLR7rxT2rw5N1ZdLX3yk/HkAyCAv05RnjIZ6dFHg/ExY6LPBaV3zjnB2Jw5wQXEgWQ7WdIK59wq59wOSVMlTcq+wDk3xznXPHfqWUmHRJwjULjZs/2Il2xdukjjx8eTD4Cko04imbZskf7wh2B8woTghq8AYkMHKMrTokXSunW5sZoaafToePJBaX3oQ353xGyNjewGj7Q5WNLbWd+vboq15EpJs0uaEdBezoVvfnTeeWz0AKC9qJNIpj/+0W+AlK2qSvr0p+PJB0AoOkBRnsKmv592mlRXF30uKL3aWmnUqGA87PcASC4LibnQC82mSBom6SctnL/KzBaa2cJ1+R8WAVF44QVp5cpg/MILo88FQFpQJ5E8mzeHj/4cP146uLX+ewBRowMU5WfXLumxx4LxsWOjzwXROffcYGzevOBOikByrZbUP+v7QyQ15F9kZudI+qakic657WE/yDl3s3NumHNuWJ8+fUqSLNCq224LxgYPlgYOjD4XAGlBnUTy3H679MEHubHqaukzn4knHwAtogMU5ee556QNG3JjnTtLZ54ZTz6IxsknSz175sa2b5eefDKefIDie17SkWZ2uJnVSrpY0ozsC8xsiKSb5N/UrY0hR2DvVq6Unn46GL/kkuhzAZAm1Ekky/r1fvp7vkmTpH79os8HQKvoAEX5Cdv9e8SI4BqRSJeaGunss4NxdoNHSjjndkm6RtLDkpZJuss596qZfcfMJjZd9hNJ3SXdbWaLzGxGCz8OiE/YVL9+/VinG0CHUCeROP/7v9LWrbmxTp2kK66IJx8AraqJOwEgx44dfvfvfEx/rwzjxknTpuXGnn7aLyrO+q9IAefcLEmz8mLfyrp9TuRJAW2xdq3f/T3flCl+wwcA6ADqJBKjoUG6++5gfPJk6cADo88HwF7xlyrKy/z50pYtubFu3aQzzognH0TrxBOl/HWadu0K7xQHAERv6lT/upytrk6aMCGefAAAiMONNwbrYdeu7PwOlDE6QFFewkaVjBrl1wBF+lVVSWPGBOMPPhh9LgCAXFu2SPfeG4x//OP+TR8AAJXgtdekhx4KxqdMkXr3jj4fAAWhAxTlY/16ae7cYJzp75UlbDf4F1+U/vKX6HMBAOwxfXpwlkZtre8ABQCgEjgn/exnwXjv3tJll0WfD4CC0QGK8vHAA9Lu3bmx/feXTj01nnwQj0GDpMMPD8anT48+FwCAt327dNttwfj48Yx2AQBUjrlzpRdeCMY/8xk27QXKHB2gKA/OhXdwTZwoVVdHnw/iYyZ95CPB+MyZ0s6d0ecDAPBT3997LzdmJl16aTz5AAAQtR07pP/+72C8vl664ILo8wHQJpF3gJpZfzObY2bLzOxVM/ti1DmgDL3wgvT228H4pEnR54L4nX++1KlTbmz9emnevHjyAYBKtm2bdOutwfiYMdKhh0aeDgAAsZg6Nfw963XXBd+7ACg7cYwA3SXpS865YySdKunzZjYohjxQTu67Lxg7+WTp4IOjzwXx69XLb36VL+z3BABQWtOm+Q+hspn56X4AAFSCdeukW24JxocPl0aMiD4fAG0WeQeoc+4d59yLTbc3S1omiV6uSrZxo/T448E40wgqW9g0+GeflRoaos8FACpVa6M/BwyIPB0AAGLxi19IjY25saoq6frr/YeCAMperGuAmtlhkoZIWhBnHojZgw8G13bs1Us688x48kF5GDYsOALYOen+++PJBwAq0b33MvoTAFDZnn9emj07GJ88WTryyOjzAdAusXWAmll3SfdKus45tynk/FVmttDMFq5bty76BBGNljY/Gj9eqq2NPh+Uj6qq8FGgM2ZIu3dHnw8AVJqtW6Xf/z4YHzuW0Z8AgMqwY4f0wx8G4z17SldfHX0+ANotlg5QM+sk3/l5h3NuWtg1zrmbnXPDnHPD+vTpE22CiM7ChdKqVcF4WMcXKs+ECb4jNNu6ddKcOfHkAwCV5Pbbw0d/fvaz8eQDAEDUfv976c9/DsavvVaqq4s+HwDtFscu8Cbpt5KWOed+GvW/jzJz++3B2JAh0mGHRZ4KytD++0sjRwbjt93mRw8DAEpj3Tr/Wpvv3HOp0QCAyrBqlfTb3wbjJ5zgB2oASJQ4RoCeIekySaPNbFHT8eEY8kDc3nhDevrpYPzii6PPBeUr7Pdh6VLpxRejzwUAKsWvfuU3QMpWU8N0PwBAZchkpP/4D2nXrtx4VZX0jW8EZ6kBKHs1Uf+DzrmnJLFNGsJHfx5yiDRqVPS5oHwNHSoNGuQ7PbPddps/BwAortdflx54IBi/6CJfpwEASLupU6XFi4PxT35SOuKI6PMB0GF8bIF4rFkjPfxwMD5lCp+mIZeZdNllwfj8+eHrxwIA2s856Wc/Cy4zUlcnXXllPDkBABClt96SfvnLYLy+nnWwgQSjpwnx+OMfgzt59+rFWioIN3q01K9fMB42ihgA0H5PPSU9/3ww/tnPstkDACD9du+W/u3f/O7v+f7lX6TOnaPPCUBR0AGK6G3eLE2bFox//OMUFISrrvajg/PNni2tXRt9PgCQRtu2ST/5STDev780eXL0+QAAELXf/lZ69dVg/KKLpJNOij4fAEVDByiid889UmNjbqxzZ98BCrRkwoTg6KNdu6Q77ognHwBIm9/8RmpoCMavvVbq1Cn6fAAAiNKiRdIttwTj9fXSF74QfT4AiooOUERr0ya/eU2+iRP9FHigJV27hneS3323X1MWANB+b7wRvqzIsGHSWWdFng4AAJHavNlPcc9kcuNVVdK3vy116RJLWgCKhw5QROvWW31xyVZVJV16aSzpIGHClknYsUO66aZ48gGANMhkpO99L/imr7ZW+sY3/GZ0AACklXO+k/Pdd4PnrrhCOuGEyFMCUHx0gCI6a9ZIU6cG45MmSYccEn0+SJ7evaVLLgnGZ85kR3gAaK977pFeeSUYv+IKP+0PAIA0u/12ae7cYPyEE9j1HUgROkARnZtuCu6mV1tLUUHbfOpTwbVAMxnphhviyQcAkqyhQfrlL4Pxww/3r7cAAKTZCy+E18Hu3aX/+A+/GSuAVKADFNFYtcqP0st3ySVS377R54Pk6tFDuvzyYHzuXGnx4sjTAYDE2r3br3eWvzGhJH3zm2x8BABIt4YG6atfDS4BI0n/9m9Sv37R5wSgZOgARTRuvDFYWOrqGF2C9rnoovCO81/8wq/hAwDYu9/+NvyDowsukE48Mfp8AACIypYt0nXXSRs2BM9ddpk0alT0OQEoKTpAUXrz50tPPBGMX355cCozUIjOnaWrrw7GFy2SZs+OPh8ASJrFi6VbbgnGDzpI+uIXo88HAICoNM+ACNtDYMgQ6fOfjz4nACVHByhKq7FR+sEPgvG+ff0oPqC9zj9fGjAgGP+v/5Lefz/6fAAgKT74wL/xy5+ZUVXl1zvr3j2evAAAKDXnpB/9SJo3L3juwAP9uZqa6PMCUHJ0gKK0fvUr6d13g/FrrvGj+ID2qq4OH6W0caP0s59Fnw8AJEEm49c1a2gInrvySmnw4OhzAgAgKr/5jTRtWjDetav0059KvXtHnxOASNABitJ55RVp6tRg/OSTpfPOiz4fpM/SYuIrAAAXbElEQVQZZ0hjxwbjs2ZJzzwTfT4AUO5uuslvGpfv+OOlz3wm+nwAAIjKXXdJN98cjJtJ3/mONHBg9DkBiAwdoCiNXbv8NLr8DWk6d/Y7y5rFkxfS58tfDl9L9gc/kLZujT4fAChXjzziNz7K162br9nV1dHnBABAFKZNk3784/BzX/oSmx4BFYAOUJTGTTdJK1YE41dfLR18cPT5IL169/Y7OOZraGAqPAA0e+016d//Pfzct79NbQYApNd990nf/374uU99Srr44mjzARALOkBRfPPmSf/7v8H40UdLn/hE9Pkg/SZMkIYPD8anTfPT4QGgkjU0SNdfL23fHjx31VXS6NHR5wQAQBTuukv63vfCz40f7/emAFAR6ABFcTU0SN/6VjBeVeV3nGV6HUrBTPrGN6Ta2uC5730vfDQyAFSCdeukz31OWrs2eG70aNb9BACkk3N+Q96Wpr2PHSv967+yNBtQQegARfHs2CF99avS5s3Bc1df7UeAAqXSv79fvyff9u3SV74ibdkSfU4AEKf335f+6Z+kv/41eG7gQD8lvoo/BQEAKbN7tx8EEbbutSSdc4703e8yOAeoMPzVi+JwTvrRj6Rly4LnzjhDuvzyyFNCBfroR6UPfzgY/8tf/Bv9TCb6nAAgDps2+Wl9b74ZPLf//tJ//qfUtWv0eQEAUEobN0rXXitNnx5+fvRoNv4DKhQdoCiOX/1Kuv/+YPygg/yna4wwQRTMpK9/XRowIHju8celH/7Qd9YDQJqtWeOnti9fHjzXs6d0441Sv37R5wUAQCktXy5ddpm0YEH4+UmTpB/8QKqpiTYvAGWBXil03G23Sb/7XTDeqZMfFVpXF31OqFxdu0o/+YnUrVvw3LRp0g03RJ8TAERl5Urp05+WVq0KnttnH/8aGPYhEQAASTZrlq9/DQ3h56+4gj0pgApHByg65r77pF/8Ivzcl78sDRoUbT6AJB16qF/UPMytt0q//32k6QBAJF580Y/8DNvwqEsXX69ZjxsAkCYbN/rNUL/1Lb8nRT4z6Z//2a+JzYZHQEVj7Dfa7667/Ei7MJ/+tPSxj0WbD5BtzBg/DfTnPw+e+5//kXbulK68kj+EACRfJiP94Q/SL38ZvtZxt27ST38qDR4cfW4AAJTKk0/6zY7eey/8fF2dX+/z9NOjzQtAWaIDFG2XyfhOpf/7v/Dzkyf7T9iAuE2Z4jcCCVui4de/9lNkvvEN1gECkFybNknf/rZ/Exhmv/38hz4DB0aaFgAAJbN+vZ/VMHNmy9cceaTf8O/gg6PLC0BZ410/2mbbNj+1eM6c8PPjxklf+Qqj6lA+Pvc56YMP/IjlfDNmSO++K/34x1L37tHnBgAd8cwzfuTLu++Gn6+v96NC2fAIAJAG27b5QTi33io1NrZ83bhx0je/6fcGAIAmdICicMuX+87PsI0VJGnkSD8KhR3fUU7M/Hq0jY3hnxI/95x06aXSd77D9FAAyfD++35K++zZLV8zeLAf+bLvvtHlBQBAKWQy/u/4X/1KWreu5et69PCDccaNY0AOgAA6QLF3mYzf6f3Xv5Z27Qq/5qMflb76VXbVQ3mqqvILo++3X/gGSH/9q/TZz0qXX+6/duoUeYoAsFc7d0rTp/t6vHFjy9dddpn0+c+zvAcAINl27JD+9Cf/XnTFitavPeMMv8t7nz7R5AYgcfjLGK1bssSPMlmypOVrrr3Wv9niUzaUs6oq6Qtf8OsA/fCHwY1CMhm/Vui8edL110vDh8eTJwDky2Skhx7as3ZxS3r08DMxzjwzstQAACi6hgbp3nul+++XNmxo/dp99pG+9CVpwgTejwJoFR2gCPf2237dsMcea/ma2lr/Rmvs2MjSAjrsox+VDjxQ+trXwtcOeuMNv27oGWdIX/yiNGBA9DkCgORfox58UJo6Vfrzn1u/dtgwP9Kd9T4BAEmUyfi1re++W5o/X3Ku9eurq6WPfUz6zGek3r2jyRFAotE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      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm as my_dist                                      # import traingular dist as my_dist\n",
    "dist_type = 'Gaussian'                                                       # give the name of the distribution for labels\n",
    "mean = 0.15; stdev = 0.03                                                    # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, loc = mean, scale = stdev)                  # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, loc = mean, scale = stdev)                  # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                  # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values, loc = mean, scale = stdev)                  # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=1.1, wspace=0.2, hspace=0.3); plt.title('Sampling Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(loc = mean, scale = stdev),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(loc = mean, scale = stdev),4)) + '.')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting the Distribution\n",
    "\n",
    "Let's make a random dataset and then fit it with a Gaussian distribution.\n",
    "\n",
    "* we do $n$ random samples, Monte Carlo simulations, from the Gaussian parametric distribution with parameters $mean$ and $stdev$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "samples = my_dist.rvs(size=int(n), loc = mean, scale = stdev, random_state = 73073).tolist() # make a synthetic dataset\n",
    "\n",
    "plt.subplot(1,2,1)                                                 # plot the binned PDF\n",
    "plt.hist(samples,bins = np.linspace(mean-3*stdev,mean+3*stdev,30), density = True, color = 'darkorange', edgecolor = 'black', alpha = 0.8)\n",
    "plt.xlim(0.0,0.3); plt.ylim(0,25); plt.xlabel('Values'); plt.ylabel('Density'); plt.title('Normalized Histogram')\n",
    " \n",
    "plt.subplot(1,2,2)                                                 # plot the CDF\n",
    "plt.hist(samples, bins = len(samples), density = True, color = 'darkorange', edgecolor = 'black', cumulative = True, histtype = 'stepfilled',alpha = 0.8)\n",
    "plt.xlim([np.min(samples),np.max(samples)]); plt.ylim(0,1); plt.xlabel('Values'); plt.ylabel('Cumulative Probability'); plt.title('CDF')\n",
    " \n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.1, wspace=0.2, hspace=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MLE mean = 0.151, MLE standard deviation = 0.028\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)                                                 # plot the binned PDF\n",
    "plt.hist(samples,bins = np.linspace(mean-3*stdev,mean+3*stdev,30), density = True, color = 'darkorange', edgecolor = 'black', alpha = 0.8)\n",
    "plt.xlim(0.0,0.3); plt.ylim(0,25); plt.xlabel('Values'); plt.ylabel('Density'); plt.title('Normalized Histogram and MLE Parametric Distribution Fit')\n",
    " \n",
    "x = np.linspace(my_dist.ppf(0.0001, loc = mean, scale = stdev),my_dist.ppf(0.9999, loc = mean, scale = stdev), 100)\n",
    "\n",
    "fit_mean, fit_stdev = my_dist.fit(samples,loc = mean, scale = stdev) # fit MLE of the distribution parameters\n",
    "print('MLE mean = ' + str(round(fit_mean,3)) + ', MLE standard deviation = ' + str(round(fit_stdev,3)))\n",
    "\n",
    "plt.plot(x, my_dist.pdf(x, loc = fit_mean, scale = fit_stdev), 'black', lw=5, alpha=0.8, label='norm pdf')\n",
    "plt.xlim(0.0,0.3); plt.ylim(0,25); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "\n",
    "plt.subplot(1,2,2)                                                 # plot the binned PDF with the fit parametric distribution\n",
    "plt.hist(samples, bins = len(samples), density = True, color = 'darkorange', edgecolor = 'black', cumulative = True, histtype = 'stepfilled',alpha = 0.8)\n",
    "plt.xlim([np.min(samples),np.max(samples)]); plt.ylim(0,1); plt.xlabel('Values'); plt.ylabel('Cumulative Probability'); plt.title('CDF and MLE Parametric Distribution Fit')\n",
    "                                                                    \n",
    "plt.plot(x, my_dist.cdf(x, loc = fit_mean, scale = fit_stdev), 'black', lw=5, alpha=0.8, label='norm pdf') # plot the CDF with the fit parametric distribution\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.1, wspace=0.2, hspace=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Fitting a Parametric Distribution by Calculating the Parameters from the Data\n",
    "\n",
    "What if we just calculate the mean and standard deviation from the sample data to use as our 'fit' parametric distribution?\n",
    "\n",
    "* this may work well if there are no outliers, e.g., if there are a couple very high values the mean would shift up and the over distribution fit would be poor\n",
    "\n",
    "* in this case we get about the same results as the maximum likelihood estimation of the distribution parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample data mean = 0.151, MLE standard deviation = 0.028\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(1,2,1)                                                 # plot the binned PDF\n",
    "plt.hist(samples,bins = np.linspace(mean-3*stdev,mean+3*stdev,30), density = True, color = 'darkorange', edgecolor = 'black', alpha = 0.8)\n",
    "plt.xlim(0.0,0.3); plt.ylim(0,25); plt.xlabel('Values'); plt.ylabel('Density'); plt.title('Normalized Histogram and Sample Statistics-based Parametric Distribution Fit')\n",
    " \n",
    "x = np.linspace(my_dist.ppf(0.0001, loc = mean, scale = stdev),my_dist.ppf(0.9999, loc = mean, scale = stdev), 100)\n",
    "\n",
    "mean = np.mean(samples); stdev = np.std(samples)\n",
    "\n",
    "print('Sample data mean = ' + str(round(mean,3)) + ', MLE standard deviation = ' + str(round(stdev,3)))\n",
    "\n",
    "plt.plot(x, my_dist.pdf(x, loc = mean, scale = stdev), 'black', lw=5, alpha=0.8, label='norm pdf')\n",
    "plt.xlim(0.0,0.3); plt.ylim(0,25); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "\n",
    "plt.subplot(1,2,2)                                                 # plot the binned PDF with the fit parametric distribution\n",
    "plt.hist(samples, bins = len(samples), density = True, color = 'darkorange', edgecolor = 'black', cumulative = True, histtype = 'stepfilled',alpha = 0.8)\n",
    "plt.xlim([np.min(samples),np.max(samples)]); plt.ylim(0,1); plt.xlabel('Values'); plt.ylabel('Cumulative Probability'); plt.title('CDF and Statistics-based Parametric Distribution Fit')\n",
    "                                                                    \n",
    "plt.plot(x, my_dist.cdf(x, loc = mean, scale = stdev), 'black', lw=5, alpha=0.8, label='norm pdf') # plot the CDF with the fit parametric distribution\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.1, wspace=0.2, hspace=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are many other parametric distributions that we could have included, but I have met my goal of providing a concise demonstration of distribution fitting. \n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of fitting parametric distributions. \n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at [Python Demos](https://github.com/GeostatsGuy/PythonNumericalDemos) and a Python package for data analytics and geostatistics at [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy). \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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